%0 Journal Article %@ 0022-1120 %A Page, MA %A Johnson, ER %D 2009 %F discovery:101256 %I CAMBRIDGE UNIV PRESS %J J FLUID MECH %K BOUNDARY, FLUID %P 299 - 309 %T Steady nonlinear diffusion-driven flow %U https://discovery.ucl.ac.uk/id/eprint/101256/ %V 629 %X An imposed normal temperature gradient on a sloping surface in a viscous stratified fluid can generate a slow steady flow along a thin 'buoyancy layer' against that surface, and in a contained fluid the associated mass flux leads to a broader-scale,outer flow'. Previous analysis for small values of the Wunsch-Phillips parameter R is extended to the nonlinear case in a contained fluid, when the imposed temperature gradient is comparable with the background temperature gradient. As for the linear case, a compatibility condition relates the buoyancy-layer mass flux along each sloping boundary to the outer-flow temperature gradient. This condition allows the leading-order flow to be determined throughout the container for a variety of configurations. %Z © 2009 Cambridge University Press